Knot theory of complex plane curves

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dc.creatorRudolph, Lee
dc.date2004-11-05
dc.date2004-11-07
dc.date.accessioned2026-07-07T05:13:59Z
dc.date.available2026-07-07T05:13:59Z
dc.descriptionThe primary objects of study in the ``knot theory of complex plane curves'' are C-links: links (or knots) cut out of a 3-sphere in the complex plane by complex plane transverse and totally tangential. Transverse C-links are naturally oriented. There are many natural classes of examples: links of singularities; links at infinity; links of divides, free divides, tree divides, and graph divides; and--most generally--quasipositive links. Totally tangential C-links are unoriented but naturally framed; they turn out to be precisely the real-analytic Legendrian links, and can profitably be investigated in terms of certain closely associated transverse C-links. The knot theory of complex plane curves is attractive not only for its own internal results, but also for its intriguing relationships and interesting contributions elsewhere in mathematics. Within low-dimensional topology, related subjects include braids, concordance, polynomial invariants, contact geometry, fibered links and open books, and Lefschetz pencils. Within low-dimensional algebraic and analytic geometry, related subjects include embeddings and injections of the complex line in the complex plane, line arrangements, Stein surfaces, and Hilbert's 16th problem.
dc.description26 figures; to appear in Handbook of Knot Theory (W. Menasco and M. Thistlethwaite, eds.)
dc.identifierhttps://arxiv.org/abs/math/0411115
dc.identifierhttp://arxiv.org/abs/math/0411115
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/73116
dc.subjectGeometric Topology
dc.subjectAlgebraic Geometry
dc.subject57M25 (Primary) 14B05, 20F36, 32S22, 32S55, 51M99 (Secondary)
dc.titleKnot theory of complex plane curves
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